### Mauscript: A Bayesian framework for performance assessment and comparison
###            of imaging biomarker quantification methods
### Authors: Brian J Smith and Reinhard R Beichel
### File Description: R code for manuscript results
### Date Modified: October 13, 2017

### Installation of companion R package qibm
### Source and instructions: https://github.com/brian-j-smith/qibm
library(devtools)
install_github("brian-j-smith/qibm")

### Load required packages
### Note that required software JAGS (http://mcmc-jags.sourceforge.net/)
###   must be installed separately
library(dplyr)
library(ggplot2)
library(qibm)

### Load dataset
data(hnc)

### Figure 1
x11(7,6)
ggplot(hnc, aes(method, Volume)) +
  geom_boxplot() +
  labs(x = "Segmentation Method",
       y = "Volume (ml)")

### Bayesian model fit
### Burnin includes an adaptation sequence of 1000 non-MCMC iterations
help(qibm)
fit <- qibm(log(Volume) ~ method, lesion, operator, data = hnc,
             n.burnin = 6000,
             n.iter = 205000,
             n.thin = 20,
             n.chains = 1,
             priors = list(sigma.opr.lim = c(0, 2),
                           sigma.imgopr.lim = c(0, 2),
                           sigma.err.lim = c(0, 2)))

### Table 2
with(fit, exp(mu)) %>% describe %>% print(digits = 2)
with(fit, exp(sqrt(diag(Sigma.img)))) %>% describe %>% print(digits = 2)
with(fit, exp(sqrt(sigma.opr^2 + sigma.imgopr^2))) %>% describe %>%
  print(digits = 2)
with(fit, exp(sigma.err)) %>% describe %>% print(digits = 2)

### Table 3
Cor(fit) %>% describe %>% print(digits = 3)

### Table 4
Bias(fit, log = TRUE) %>% describe %>% print(digits = 2)
CIndex(fit) %>% describe %>% print(digits = 2)
ICC(fit) %>% describe %>% print(digits = 2)
wCV(fit, log = TRUE) %>% describe %>% print(digits = 2)
RDC(fit) %>% describe %>% print(digits = 2)
RC(fit) %>% describe %>% print(digits = 2)

### Table 5
x <- describe(with(fit, mu))$Mean[1]
scale <- describe(with(fit, sqrt(diag(Sigma.img))))$Mean[1]
coef <- LRMCoef(1.5, scale = scale, p = 0.5, x = x)
fit.LRM <- LRM(fit, N = c(250, 500), coef = coef)
fit.LRM %>% describe(scale = scale) %>% print(digits = 3)

### Posterior predictive p-values
GOF(fit) %>% describe %>% print(digits = 3)

### Figure 2
x11(7,6)
plot(GOF(fit, select = 1))